| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2021 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Identify and compare sampling techniques |
| Difficulty | Easy -1.2 This is a straightforward AS-level statistics question requiring only basic recall and simple calculations: naming a sampling technique (self-selection/volunteer sampling), stating a disadvantage, multiplying frequency densities by class widths to verify sample size, and calculating a simple probability from grouped data. No problem-solving insight or complex reasoning required. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc2.02a Interpret single variable data: tables and diagrams2.02b Histogram: area represents frequency |
| Time spent using social media in minutes | \(0 -\) | \(15 -\) | \(30 -\) | \(60 -\) | \(120 - 240\) |
| Number of people per minute | 12.2 | 14.0 | 8.4 | 7.3 | 3.1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| This is a self-selecting sample | B1 | Syllabus says 'self-selected' |
| it may introduce bias | B1 | Or an explanation of why the sample is biased |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(12.2\times15 + 14\times15 + 8.4\times30 + 7.3\times60 + 3.1\times120\) | M1 | at least 3 correct terms |
| \(= 1455\) | A1 | AG WWW. May see \(183 + 210 + 252 + 438 + 372\) |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\frac{7.3\times60 + 3.1\times120}{1455}\) | M1 | |
| \(= \frac{54}{97}\) or \(0.5567\) correct to 2, 3 or 4 sf | A1 | |
| [2] |
## Question 11:
### Part (a):
| Answer | Mark | Guidance |
|--------|------|----------|
| This is a self-selecting sample | B1 | Syllabus says 'self-selected' |
| it may introduce bias | B1 | Or an explanation of why the sample is biased |
| **[2]** | | |
### Part (b):
| Answer | Mark | Guidance |
|--------|------|----------|
| $12.2\times15 + 14\times15 + 8.4\times30 + 7.3\times60 + 3.1\times120$ | M1 | at least 3 correct terms |
| $= 1455$ | A1 | AG WWW. May see $183 + 210 + 252 + 438 + 372$ |
| **[2]** | | |
### Part (c):
| Answer | Mark | Guidance |
|--------|------|----------|
| $\frac{7.3\times60 + 3.1\times120}{1455}$ | M1 | |
| $= \frac{54}{97}$ or $0.5567$ correct to 2, 3 or 4 sf | A1 | |
| **[2]** | | |
---11 James is investigating the amount of time retired people spend each day using social media. He collects a sample by advertising in a local newspaper for people to complete an online survey.
\begin{enumerate}[label=(\alph*)]
\item State
\begin{itemize}
\item the name of the sampling technique he is using,
\item one disadvantage of using this technique.
\end{itemize}
James processes his data in order to draw a histogram. His table of results is shown below.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Time spent using social media in minutes & $0 -$ & $15 -$ & $30 -$ & $60 -$ & $120 - 240$ \\
\hline
Number of people per minute & 12.2 & 14.0 & 8.4 & 7.3 & 3.1 \\
\hline
\end{tabular}
\end{center}
\item Show that the size of the sample is 1455 .
\item Calculate an estimate of the probability that a retired person spends more than an hour per day using social media.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2021 Q11 [6]}}